If we are going to define an interval to mean one or the other
(1) that interval of time, or
(2) when an event occurred, e.g. "it occurred sometime between 1964 and 2008")
The we need to go with (1), because that's how ISO 8601 defines it.
(Aside: although that itself isn't completely clear, but is "best interpretation. And, it isn't clear that ISO 8601 has the same concept of precision as we seem to be adopting; 8601 would see 1964/2008 as meaning the interval starting at the very beginning of 1964 and ending at the very end of 2008, while we see it as the interval beginning sometime in 1964 and ending sometime in 2008. However, 8601 isn't even completely clear on that point, and I have no problem with our view.)
But look at it this way: suppose you want to say "the event occurred at some intant between 1964 and 2008". The data element that you are saying this for could have a definition like "the interval within which the event occurred".
So as you say "you are not allowing people to unambiguously state whether they are referring to an interval or a point in time within that interval". Is that really necessary? When you state a dateTime expression, there has to be some context, doesn't there? In other words, you are stating it as the value of a data element, right? And the data elements definition would dictate which interpretation applies.